Geometry and Measurement

Classify angles

Acute, obtuse, right, and straight angles
o Acute angles measure less than 90 degrees
o Obtuse angles measure more than 90 degrees
o Right angles measure exactly 90 degrees
o Straight angles measure exactly 180 degrees

Complementary angles
o Complementary angles are angles whose sum equal 90 degrees

Supplementary angles
o Supplementary angles are angles whose sum equal 180 degrees

Vertical angles
o Vertical angles are formed by intersecting two lines, and the opposite angles are equal

Classify triangles

Classify by sides
o Equilateral triangles have all equal sides of measurement
o Isosceles triangles have two equal sides of measurement
o Scalene triangles have different sides of measurement

Classify by angles
o Acute triangles are triangles with all acute angles
o Obtuse triangles are triangles with one obtuse angle
o Right triangles are triangles with one right angle

Sum of all angles = 180 degrees

Perimeter of triangles
o The perimeter is the distance around the shape.
o To determine the perimeter of a triangle, add the measurements of all three sides.

Area of triangles
o To determine the area of a triangle, multiply the base times the height, and then divide that product by two. The formula is: A = (b x h)/2
o Area units are always squared.

Classify polygons

Classify by number of sides
3-sides – triangles
4-sides – quadrilaterals
5-sides – pentagons
6-sides – hexagons
8-sides – octagons
10-sides – decagons
12-sides – dodecagons

Circles

Radius, diameter
o The radius is the measurement from the center of the circle to any point on the circle.
o The diameter is the measurement from two points on the circle, where the line passes through the center.

Circumference of circle
o The circumference of a circle is the distance around the circle.
o To determine the circumference, multiply the diameter of the circle times pi (approximate value of 3.14).

Area of circle
o The area of a circle is the measurement of the space inside the circle.
o To determine the area, square the radius, and multiply by pi (approximate value of 3.14).
o Area units are always squared.

Pythagorean Theorem

The Pythagorean Theorem only applies to right triangles
The Pythagorean Theorem is used to determine the distance of one of the sides of a right triangle when the other two distances are known.

• The side opposite of the right angle is known as the hypotenuse, and it is labeled as “c.”
• The other two sides of the right triangle are known as the legs, and they are labeled as “a” and “b” – in no particular order.
• Use the formula a^2 + b^2 = c^2, where ^ means to square.
o Use the property of equality of solve for the missing value.

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